Time-domain adaptive harmonic control for rejection of sinusoidal disturbances acting on an unknown discrete-time system

We consider the problem of rejecting sinusoids with known frequencies that act on a completely unknown multi-input multi-output linear time-invariant system. First, we present a new time-domain harmonic control (TD-HC) approach, which is effective for rejecting sinusoids with known frequencies but requires an estimate of the control-to-performance transfer function evaluated at the disturbance frequencies. We analyze the stability of TD-HC, and perform a numerical comparison between TD-HC and an existing control approach (i.e., higher harmonic control), which requires exactly the same model information. This comparison shows that TD-HC offers reduced convergence times. Second, we address the problem of uncertainty in the model information required to implement TD-HC. We present a new time-domain adaptive harmonic control (TD-AHC) algorithm, which is effective for rejecting sinusoids with known frequencies that act on an unknown multi-input multi-output linear time-invariant system. We demonstrate TD-AHC in numerical simulations.